440 research outputs found
Casimir interaction between normal or superfluid grains in the Fermi sea
We report on a new force that acts on cavities (literally empty regions of
space) when they are immersed in a background of non-interacting fermionic
matter fields. The interaction follows from the obstructions to the (quantum
mechanical) motions of the fermions caused by the presence of bubbles or other
(heavy) particles in the Fermi sea, as, for example, nuclei in the neutron sea
in the inner crust of a neutron star or superfluid grains in a normal Fermi
liquid. The effect resembles the traditional Casimir interaction between
metallic mirrors in the vacuum. However, the fluctuating electromagnetic fields
are replaced by fermionic matter fields. We show that the fermionic Casimir
problem for a system of spherical cavities can be solved exactly, since the
calculation can be mapped onto a quantum mechanical billiard problem of a
point-particle scattered off a finite number of non-overlapping spheres or
disks. Finally we generalize the map method to other Casimir systems,
especially to the case of a fluctuating scalar field between two spheres or a
sphere and a plate under Dirichlet boundary conditions.Comment: 8 pages, 2 figures, submitted to the Proceedings of QFEXT'05,
Barcelona, Sept. 5-9, 200
Towards an Asymptotic-Safety Scenario for Chiral Yukawa Systems
We search for asymptotic safety in a Yukawa system with a chiral
symmetry, serving as a toy model for the
standard-model Higgs sector. Using the functional RG as a nonperturbative tool,
the leading-order derivative expansion exhibits admissible non-Ga\ssian
fixed-points for which arise from a conformal threshold
behavior induced by self-balanced boson-fermion fluctuations. If present in the
full theory, the fixed-point would solve the triviality problem. Moreover, as
one fixed point has only one relevant direction even with a reduced hierarchy
problem, the Higgs mass as well as the top mass are a prediction of the theory
in terms of the Higgs vacuum expectation value. In our toy model, the fixed
point is destabilized at higher order due to massless Goldstone and fermion
fluctuations, which are particular to our model and have no analogue in the
standard model.Comment: 16 pages, 8 figure
Introduction to the functional RG and applications to gauge theories
These lectures contain an introduction to modern renormalization group (RG)
methods as well as functional RG approaches to gauge theories. In the first
lecture, the functional renormalization group is introduced with a focus on the
flow equation for the effective average action. The second lecture is devoted
to a discussion of flow equations and symmetries in general, and flow equations
and gauge symmetries in particular. The third lecture deals with the flow
equation in the background formalism which is particularly convenient for
analytical computations of truncated flows. The fourth lecture concentrates on
the transition from microscopic to macroscopic degrees of freedom; even though
this is discussed here in the language and the context of QCD, the developed
formalism is much more general and will be useful also for other systems.Comment: 60 pages, 14 figures, Lectures held at the 2006 ECT* School
"Renormalization Group and Effective Field Theory Approaches to Many-Body
Systems", Trento, Ital
Casimir forces between arbitrary compact objects: Scalar and electromagnetic field
We develop an exact method for computing the Casimir energy between arbitrary
compact objects, both with boundary conditions for a scalar field and
dielectrics or perfect conductors for the electromagnetic field. The energy is
obtained as an interaction between multipoles, generated by quantum source or
current fluctuations. The objects' shape and composition enter only through
their scattering matrices. The result is exact when all multipoles are
included, and converges rapidly. A low frequency expansion yields the energy as
a series in the ratio of the objects' size to their separation. As examples, we
obtain this series for two spheres with Robin boundary conditions for a scalar
field and dielectric spheres for the electromagnetic field. The full
interaction at all separations is obtained for spheres with Robin boundary
conditions and for perfectly conducting spheres.Comment: 24 pages, 3 figures, contribution to QFEXT07 proceeding
Towards a renormalizable standard model without fundamental Higgs scalar
We investigate the possibility of constructing a renormalizable standard
model with purely fermionic matter content. The Higgs scalar is replaced by
point-like fermionic self-interactions with couplings growing large at the
Fermi scale. An analysis of the UV behavior in the point-like approximation
reveals a variety of non-Gaussian fixed points for the fermion couplings. If
real, such fixed points would imply nonperturbative renormalizability and evade
triviality of the Higgs sector. For point-like fermionic self-interactions and
weak gauge couplings, one encounters a hierarchy problem similar to the one for
a fundamental Higgs scalar.Comment: 18 pages, 4 figure
Effective action for the order parameter of the deconfinement transition of Yang-Mills theories
The effective action for the Polyakov loop serving as an order parameter for
deconfinement is obtained in one-loop approximation to second order in a
derivative expansion. The calculation is performed in dimensions,
mostly referring to the gauge group SU(2). The resulting effective action is
only capable of describing a deconfinement phase transition for
. Since, particularly in , the system is
strongly governed by infrared effects, it is demonstrated that an additional
infrared scale such as an effective gluon mass can change the physical
properties of the system drastically, leading to a model with a deconfinement
phase transition.Comment: 23 pages, 4 figures, minor improvements, version to appear in PR
Equivalent Fixed-Points in the Effective Average Action Formalism
Starting from a modified version of Polchinski's equation, Morris'
fixed-point equation for the effective average action is derived. Since an
expression for the line of equivalent fixed-points associated with every
critical fixed-point is known in the former case, this link allows us to find,
for the first time, the analogous expression in the latter case.Comment: 30 pages; v2: 29 pages - major improvements to section 3; v3:
published in J. Phys. A - minor change
Scaling laws near the conformal window of many-flavor QCD
We derive universal scaling laws for physical observables such as the
critical temperature, the chiral condensate, and the pion decay constant as a
function of the flavor number near the conformal window of many-flavor QCD in
the chiral limit. We argue on general grounds that the associated critical
exponents are all interrelated and can be determined from the critical exponent
of the running gauge coupling at the Caswell-Banks-Zaks infrared fixed point.
We illustrate our findings with the aid of nonperturbative functional
Renormalization Group (RG) calculations and low-energy QCD models.Comment: 18 pages, 4 figures, references added and discussion expanded
(matches JHEP version
Exact zero-point interaction energy between cylinders
We calculate the exact Casimir interaction energy between two perfectly
conducting, very long, eccentric cylindrical shells using a mode summation
technique. Several limiting cases of the exact formula for the Casimir energy
corresponding to this configuration are studied both analytically and
numerically. These include concentric cylinders, cylinder-plane, and eccentric
cylinders, for small and large separations between the surfaces. For small
separations we recover the proximity approximation, while for large separations
we find a weak logarithmic decay of the Casimir interaction energy, typical of
cylindrical geometries.Comment: 20 pages, 7 figure
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